The key question, as GD727 pointed out, is: Does "airports" include small airfields or just commercial airports with regularly scheduled airline service?
If it's the latter, then you don't really need to collect data on each and every airport that is served by the airlines. You can just take a sample of airports from, say, every region of the country (I'm assuming of course that you mean only U.S. airports). You can take, for example, runway lengths of 5 airports on the West Coast, 6 in the Midwest, 7 in the East Coast, 6 from Southern airports, etc. and then just figure out your average from that. If you did it right, it should repreent the majority of runway lengths for most of the major airports in the U.S.. It also represents its average.
Its better to be on the ground wishing you were in the air than be in the air wishing you were on the ground. Fly safe!